Transcript NEWTON`s SECOND LAW

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WHEN FORCES ARE NOT BALANCED
A RESULTANT FORCE CHANGES A
BODY’S VELOCITY
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NEWTON’S SECOND LAW :
“THE RATE OF CHANGE OF
MOMENTUM OF A BODY IS
DIRECTLY PROPORTIONAL TO
THE RESULTANT EXTERNAL
FORCES ACTING UPON IT, AND
TAKES PLACE IN THE
DIRECTION OF THAT FORCE”
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A RESULTANT FORCE PRODUCES A CHANGE
IN A BODY’S MOMENTUM
A RESULTANT FORCE
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AN
ACCELERATION
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p
F
t
NEWTON 2
 ( mv)
F
t
If u = initial velocity, v = final velocity and t = time for the change, then
mv  mu
F
t
F
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 ma
m (v  u )
F
t
v u
but acceleration, a 
t
F = k ma
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F = k ma
OUR UNIT OF FORCE, THE NEWTON,
IS DEFINED SO THAT k = 1
ONE NEWTON IS THE FORCE THAT CAUSES
A MASS OF 1 kg TO ACCELERATE AT 1 m/s2
F=kma so 1 = k x 1 x 1
so k = 1
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NEWTON’S SECOND LAW
units
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• F
in
Newtons
• m
in
kilograms
• a
in
metres per second2
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ACCELERATION IS DIRECTLY PROPORTIONAL TO THE APPLIED FORCE
acceleration / ms-2
force / N
N.B. - STRAIGHT LINE THROUGH THE ORIGIN
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GRAPH OF ACCELERATION VERSUS MASS
acceleration / ms-2
mass / kg
F=ma
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1
a
m
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ACCELERATION IS INVERSELY PROPORTIONAL TO MASS OF THE BODY
acceleration / ms-2
1
/ kg 1
m
N.B. - STRAIGHT LINE THROUGH THE ORIGIN
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NEWTON’S SECOND LAW IS USED IN TWO FORMS
F  ma
Where F is the
RESULTANT FORCE
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 (mv)
F
t
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QUESTION
A railway engine pulls a wagon of mass 10 tonnes along a level
track at a constant velocity. The pull force in the couplings
between the engine and wagon is 1000 N.
(A)
What is the force opposing the motion of the wagon?
(B)
If the pull force is increased to 1400 N and the
resistance to movement of the wagon remains constant,
what would be the acceleration of the wagon?
The speed is steady, so by Newton’s first law, the
resultant force must be zero. The pull on the wagon
must equal the resistance to motion. Answer is 1000 N
The resultant force on the wagon is 1400 – 1000 = 400 N
.
Acceleration = Force ÷ mass = 400 ÷ 10 000 = 0.04 ms-2
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IMPULSE
IMPULSE = the product of a
force and the time that the
force is applied for.
UNITS = Newton seconds , Ns .
mv  mu
F
t
Ft = mv - mu
IMPULSE = CHANGE OF MOMENTUM
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Force-Time Graphs
The force applied to a body is rarely constant. Physicists
tend to consider the force as a function of time and plot a
graph of Force versus Time.
force / N
Time / s
Impulse = Area under the graph
= Change in momentum
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Collision B
Collision A
“I’ve just crashed into
a brick wall!”
“I’ve just crashed
into a haystack!”
BOTH CARS HAD THE SAME MASS AND WERE
TRAVELLING AT THE SAME SPEED
force / N
B
A
Time / s
IDENTIFY WHICH COLLISIONS IS A AND WHICH IS B.
COMMENT ON THE INFORMATION PROVIDED BY THE TWO GRAPHS
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